A151579 - OEIS

%I #7 May 06 2020 01:37:49

%S 0,7,960,38637,882340,14413894,188690976,2112659718,21078701112,

%T 192648942945,1644431982848,13295963811083,102911255502876,

%U 768689550213368,5575887557096640,39473882067826332,273820542615005232,1867156445048432043,12548621876834960064

%N Number of permutations of 1..n arranged in a circle with exactly 6 adjacent element pairs in decreasing order.

%H Andrew Howroyd, <a href="/A151579/b151579.txt">Table of n, a(n) for n = 6..500</a>

%F From _Andrew Howroyd_, May 05 2020: (Start)

%F a(n) = n*A000514(n-1).

%F a(n) = n*(6^(n-1) - n*5^(n-1) + binomial(n,2)*4^(n-1) - binomial(n,3)*3^(n-1) + binomial(n,4)*2^(n-1) - binomial(n,5)). (End)

%o (PARI) a(n) = {n*(6^(n-1) - n*5^(n-1) + binomial(n,2)*4^(n-1) - binomial(n,3)*3^(n-1) + binomial(n,4)*2^(n-1) - binomial(n,5))} \\ _Andrew Howroyd_, May 05 2020

%Y Column k=6 of A334218.

%Y Cf. A000514.

%K nonn

%O 6,2

%A _R. H. Hardin_, May 21 2009

%E Terms a(17) and beyond from _Andrew Howroyd_, May 05 2020